Variance: the average squared deviation from the mean. Its square root, the standard deviation, measures the same spread in the original units.
Card 1 of 259. Answer: Variance: the average squared deviation from the mean. Its square root, the standard deviation, measures the same spread in the original units.
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Variance. It is the average squared distance of the values from their mean: σ² = (1/N) Σ (xᵢ − μ)² for a population. Its square root, the standard deviation, gives the same spread in the original units.
Example: for 1, 3, 5, 7 and 9 the mean is 5 and the squared deviations 16, 4, 0, 4 and 16 sum to 40, so the population variance is 40 / 5 = 8. As a sample, the variance is 40 / 4 = 10: dividing by n − 1, Bessel's correction, makes it an unbiased estimate of the population variance. Deviations are squared because raw deviations always sum to zero.
Interviewers ask why n − 1: the sample mean sits closer to the data than the true mean does, so dividing by n underestimates spread. Also worth knowing: Var(aX + b) = a² Var(X), variances of independent variables add, and squaring makes outliers weigh heavily. A practical trap: NumPy's var divides by n by default, pandas by n − 1.
